They are separate.
Trail rations are made up of foodstuffs that are preserved or that can otherwise be stretched out to last over a long journey. They are compact and easily stored. Water isn't something that can be preserved in such a way — it can't be compressed and, obviously, you can't dehydrate it. Water kept for too long becomes unpalatable, and may be a vector for disease. Moreover, travelers need more water than food, as dehydration sets in before hunger and starvation would.
In sum, the amount of water one needs for a day's journey takes up more space than a corresponding amount of food, and so "a week's worth of water" would be inconvenient to carry on one's back or pack animals in a way that "a week's worth of food" would not.
Problem 1 - rations are listed by weight, while barrels are listed by volume
Problem 2 - D&D uses American units, which makes the math less obvious.
So, step 1, gather data.
1 pound ≅ 0.45 kg
1 gal ≅ 3.8 liters
food tends to run a specific gravity between 0.8 and 1.5, with some exception on both ends.
So, with a 2 lb ≅ 0.9 kg; 2.2 lb ≅ 1 kg
At a rough SG 1.1, that's about 1L
40 gal ≅ 152 l
thus about 152 rations
If it's a 1 lb ration, it's about 304 rations in a 40 gallon barrel.
In either case, packing loss for cuboid solids in a barrel is about 20%... so about 120 rations at 2 lbs., or 240 at 1 lb.
And note that typical barrels are good for molasses or honey at about SG 1.45, so the barrel can handle about 220 kg total mass, or about 484 lbs. Both have high viscosity, tho, so don't leak through the joins... Anyway, above about 500 lbs, the barrel ends are unlikely to hold.
As for which, looking in the PBR, as it's been updated. Says 2 lb, so I do believe that's the correct and intended answer. It also matches my SCA camping experiences with hardtack, sausage, and cheese. (2 lb saussage, 5 lb cheese, and 2 lb crackers for 2 adults and two children for a weekend, with both adults plus sized, and me fighting.)
Best Answer
A ration weighs two pounds, but a character only needs to consume one pound (half a ration) per day.
The key word in this case is need and how this is very different from should. A character, at a bare minimum, needs be consuming one pound of food per day, but very rarely will anyone want to get by on the bare minimum amount of food unless it's a survival scenario and resources are scarce. It stands to reason that a ration is two pounds because consuming a whole ration would be enough food to comfortably satisfy a day's requirement of food, and therefore, what a character should consume per day.
We can very easily reword the quote to yield the following:
The word subsisting supports this interpretation because of the following definition provided by a simple Google search:
It could stand to argue that if a ration were intended to be one pound, one could not, by definition, subsist on half a ration by definition since half a pound of food is less than what is required in a day.
If that's the case, why shouldn't I only consume half rations to save resources?
As mxyzplk mentions in his comment,
We must remember that rations are intended to sustain adventures and travelers who will very likely need more than the bare minimum amount of food daily. If we consider modern body builders, they can very easily consume six meals a day as opposed to the average three because they must sustain their added muscle mass. One might be able to argue that a warrior might need more food than a wizard, but neither will be happy if they only ate only what they needed for an extended period of time.
This, unfortunately, does not offer a mechanical reason as to why a character should consume more than a pound of food a day and I am unaware of any in-game rules which address this either. This would suggest two possible solutions to encourage players to consume a full ration whenever possible:
As to which should be used and to what degree is up to the GM's discretion for what they believe is a best fit for their campaign or scenario.